Multi-scale modeling of a wound-healing cell migration assay

A continuum model and a discrete model are developed to capture the population-scale and cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in a confluent cell monolayer. During wound closure, the cell population forms a sustained traveling wave, with close contact between cells behind the wavefront. Cells exhibit contact inhibition of migration and contact-limited proliferation. The continuum model includes the two dominant mechanisms and characteristics of cell migration and proliferation, using a cell diffusivity function that decreases with cell density and a logistic proliferative growth term. The discrete model arises naturally from the continuum model. Individual cells are simulated as continuous-time random walkers with nearest-neighbor transitions, together with a birth/death process. The migration and proliferation parameters are determined by analysing individual mice 3T3 fibroblast cell trajectories obtained during the development of a confluent cell monolayer and in a wound healing assay. The population-scale model successfully predicts the shape and speed of the traveling wave, while the discrete model is also successful in capturing the contact inhibition of migration effects.     

Cell resensitization after delivery of a cycle-specific anticancer drug and effect of dose splitting: learning from tumour cords

After a single dose of an anticancer agent, changes due to cell death are expected to occur in the distribution of cells between proliferating and quiescent compartment as well as in the oxygenation and nutritional state of surviving cells. These changes are transient because tumour regrowth tends to restore the pretreatment status. The reoxygenation due to the decrease of oxygen consumption is expected to induce cell recruitment from quiescence into proliferation, and consequently to increase the sensitivity of the cell population to a successive treatment by a cycle-specific drug. In previous papers we proposed a model of the response of tumour cords (cylindrical arrangements of tumour cells growing around a blood vessel of the tumour) to single-dose treatments. The model included the motion of cells and oxygen diffusion and consumption. On the basis of that model suitably extended to better account for the action of anticancer drugs, we study the time course of the oxygenation and of the redistribution of cells between the proliferating and quiescent compartments. By means of simulations of the response to a dose delivered as two spaced equal fractions, we investigate the dependence of tumour response on the spacing between the fractions and on the main parameters of the system. A time window may be found in which the delivery of two fractions is more effective than the delivery of the undivided dose.     

Stimulus-dependent state transition between synchronized oscillation and randomly repetitive burst in a model cerebellar granular layer

Information processing of the cerebellar granular layer composed of granule and Golgi cells is regarded as an important first step toward the cerebellar computation. Our previous theoretical studies have shown that granule cells can exhibit random alternation between burst and silent modes, which provides a basis of population representation of the passage-of-time (POT) from the onset of external input stimuli. On the other hand, another computational study has reported that granule cells can exhibit synchronized oscillation of activity, as consistent with observed oscillation in local field potential recorded from the granular layer while animals keep still. Here we have a question of whether an identical network model can explain these distinct dynamics. In the present study, we carried out computer simulations based on a spiking network model of the granular layer varying two parameters: the strength of a current injected to granule cells and the concentration of Mg²⁺ which controls the conductance of NMDA channels assumed on the Golgi cell dendrites. The simulations showed that cells in the granular layer can switch activity states between synchronized oscillation and random burst-silent alternation depending on the two parameters. For higher Mg²⁺ concentration and a weaker injected current, granule and Golgi cells elicited spikes synchronously (synchronized oscillation state). In contrast, for lower Mg²⁺ concentration and a stronger injected current, those cells showed the random burst-silent alternation (POT-representing state). It is suggested that NMDA channels on the Golgi cell dendrites play an important role for determining how the granular layer works in response to external input.     

Possibility of tissue separation caused by cell adhesion

Adhesive molecules are suggested to play an important role when a single tissue is separated into two in developmental processes, illustrated by tissue-specific cadherins in the neural tube formation of amphibians. In this paper, we study the possibility for tissue separation to be carried out only by differential cell adhesion and random cell movement without any other morphogenetic mechanisms. We consider a two-dimensional regular triangular lattice filled with cells of three types (black, white, and gray). In the initial state, a cluster of black cells and a cluster of white cells are in contact and are surrounded by gray cells. Nearest-neighbor cells exchange their location at random, but the movement occurs faster if it increases the total adhesion. We considered separation to be successful if, in the final state, black cells and white cells kept their clusters but two clusters lost their direct contact with each other as gray cells are inserted between them. The maximum total adhesion (MTA) rule conjectures that the spatial pattern achieving maximum total adhesion might be that obtained in the final state. In the computer simulation, the runs for successful separation satisfied the condition predicted by the MTA rule. However, the condition for successful separation was more restricted than that predicted by the MTA rule. For some combinations of adhesions, it took an extremely long time to accomplish tissue separation. Finally, we discuss the role of homophilic adhesion molecules (such as cadherins) in the tissue separation processes, and show that the new expression of homophilic adhesion molecules cannot perform tissue separation without the change in other morphogenetic processes.     

Memory in idiotypic networks due to competition between proliferation and differentiation

A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation preceeds differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a “mexican-hat” effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively chanbed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.     

Formulation and numerical simulations of a continuum model of avascular tumor growth

In this paper we present a continuum mathematical model for a multicellular spheroid that mimics the micro-environment within avascular tumor growth. The model consists of a coupled system of non-linear convection-diffusion-reaction equations. This system is solved using a previously developed conservative Galerkin characteristics method. In the model considered, there are three cell types: the proliferative cells, the quiescent non-dividing cells which stay in the G₀ phase of the cell cycle and the necrotic cells. The model includes viable cell diffusion, diffusion of cellular material and the removal of necrotic cells. We assume that the nutrients diffuse passively and are consumed by the proliferative and quiescent tumor cells depending on the availability of resources (oxygen, glucose, etc.). The numerical simulations are performed using different sets of parameters, including biologically realistic ones, to explore the effects of each of these model parameters on reaching the steady state. The present results, taken together with those reported earlier, indicate that the removal of necrotic cells and the diffusion of cellular material have significant effects on the steady state, reflecting growth saturation, the number of viable cells, and the spheroid size.     

An artificial antigen-presenting cell with paracrine delivery of IL-2 impacts the magnitude and direction of the T cell response

Artificial antigen-presenting cells (aAPCs) are an emerging technology to induce therapeutic cellular immunity without the need for autologous antigen-presenting cells (APCs). To fully replace natural APCs, an optimized aAPC must present antigen (signal 1), provide costimulation (signal 2), and release cytokine (signal 3). Here we demonstrate that the spatial and temporal characteristics of paracrine release of IL-2 from biodegradable polymer aAPCs (now termed paAPCs) can significantly alter the balance in the activation and proliferation of CD8+ and CD4+ T cells. Paracrine delivery of IL-2 upon T cell contact with paAPCs induces significant IL-2 accumulation in the synaptic contact region. This accumulation increases CD25 (the inducible IL-2 Rα chain) on responding T cells and increases proliferation of CD8+ T cells in vitro to levels 10 times that observed with equivalent amounts of bulk IL-2. These CD8+ T cell responses critically depend upon close contact of T cells and the paAPCs and require sustained release of low levels of IL-2. The same conditions promote activation-induced cell death in CD4+ T cells. These findings provide insight into the response of T cell subsets to paracrine IL-2.     

An in silico investigation into the causes of telomere length heterogeneity and its implications for the Hayflick limit

In telomerase-negative cell populations the mean telomere length (TL) decreases with increasing population doubling number (PD). A critically small TL is believed to stop cell proliferation at a cell-, age- and species-specific PD thus defining the Hayflick limit. However, positively skewed TL distributions are broad compared to differences between initial and final mean TL and strongly overlap at middle and late PD, which is inconsistent with a limiting role of TL. We used computer-assisted modelling to define what set of premises may account for the above. Our model incorporates the following concepts. DNA end replication problem: telomeres loose 1 shortening unit (SU) upon each cell division. Free radical-caused TL decrease: telomeres experience random events resulting in the loss of a random SU number within a remaining TL. Stochasticity of gene expression and cell differentiation: cells experience random events inducing mitoses or committing cells to proliferation arrest, the latter option requiring a specified number of mitoses to be passed. Cells whose TL reaches 1SU cannot divide. The proliferation kinetics of such virtual cells conforms to the transition probability model of cell cycle. When no committing events occur and at realistic SU estimates of the initial TL, maximal PD values far exceed the Hayflick limit observed in normal cells and are consistent with the crisis stage entered by transformed cells that have surpassed the Hayflick limit. At intermediate PD, symmetrical TL distributions are yielded. Upon introduction of committing events making the ratio of the rates of proliferating and committing events (P/C) range from 1.10 to 1.25, TL distributions at intermediate PD become positively skewed, and virtual cell clones show bimodal size distributions. At P/C as high as 1.25 the majority of virtual cells at maximal PD contain telomeres with TL>1SU. A 10% increase in P/C within the 1.10-1.25 range produces a two-fold increase in the maximal PD, which can reach values of up to 25 observed in rodent and some human cells. Increasing the number of committed mitoses from 0 to 10 can increases PD to about 50 observed in human fibroblasts. Introduction of the random TL breakage makes the shapes of TL distributions quite dissimilar from those observed in real cells. CONCLUSIONS: Telomere length decrease is a correlate of cell proliferation that cannot alone account for the Hayflick limit, which primarily depends on parameters of cell population kinetics. Free radical damage influences the Hayflick limit not through TL but rather by affecting the ratio of the rates of events that commit cells to mitoses or to proliferation arrest.     

Src Induces Podoplanin Expression to Promote Cell Migration

Nontransformed cells can force tumor cells to assume a normal morphology and phenotype by the process of contact normalization. Transformed cells must escape this process to become invasive and malignant. However, mechanisms underlying contact normalization have not been elucidated. Here, we have identified genes that are affected by contact normalization of Src-transformed cells. Tumor cells must migrate to become invasive and malignant. Src must phosphorylate the adaptor protein Cas (Crk-associated substrate) to promote tumor cell motility. We report here that Src utilizes Cas to induce podoplanin (Pdpn) expression to promote tumor cell migration. Pdpn is a membrane-bound extracellular glycoprotein that associates with endogenous ligands to promote tumor cell migration leading to cancer invasion and metastasis. In fact, Pdpn expression accounted for a major part of the increased migration seen in Src-transformed cells. Moreover, nontransformed cells suppressed Pdpn expression in adjacent Src-transformed cells. Of >39,000 genes, Pdpn was one of only 23 genes found to be induced by transforming Src activity and suppressed by contact normalization of Src-transformed cells. In addition, we found 16 genes suppressed by Src and induced by contact normalization. These genes encode growth factor receptors, adaptor proteins, and products that have not yet been annotated and may play important roles in tumor cell growth and migration.     

Attachment of columnar airway epithelial cells in asthma

Shedding of airway epithelial cells is a common finding in asthma. In this study, the attachment of the airway epithelial cells to the basal lamina (BL) was investigated by transmission electron microscopy (TEM) of biopsies from patients with atopic asthma and healthy controls. The following parameters were quantitatively determined: the height of the epithelium and of the columnar cells, the number of basal cells per 100 microm of basal lamina, the contact surfaces of basal cells or columnar cells with the basal lamina, and between basal cells and columnar cells. In order to compare the quantitative method with previous literature data, measurements were also carried out on rat airway epithelium. Compared to the rat, the columnar cell height in the human is increased, basal cells are smaller, and there is a larger contact area between basal cells and basal lamina, as well as between basal and columnar cells. The contact area between columnar cells and basal lamina is hence less in the human airway. The contact area between columnar cells and basal lamina in asthmatics is significantly less than in healthy controls, due to larger intercellular spaces. It is concluded that attachment of columnar cells to the basal lamina occurs mainly indirectly, via desmosomal attachment to basal cells, and that direct attachment of columnar cells to the basal lamina is weakened in asthmatics.     

Folding and stability of helical bundle proteins from coarse‐grained models

We develop a coarse‐grained model where solvent is considered implicitly, electrostatics are included as short‐range interactions, and side‐chains are coarse‐grained to a single bead. The model depends on three main parameters: hydrophobic, electrostatic, and side‐chain hydrogen bond strength. The parameters are determined by considering three level of approximations and characterizing the folding for three selected proteins (training set). Nine additional proteins (containing up to 126 residues) as well as mutated versions (test set) are folded with the given parameters. In all folding simulations, the initial state is a random coil configuration. Besides the native state, some proteins fold into an additional state differing in the topology (structure of the helical bundle). We discuss the stability of the native states, and compare the dynamics of our model to all atom molecular dynamics simulations as well as some general properties on the interactions governing folding dynamics. Proteins 2013; 81:1200–1211. © 2013 Wiley Periodicals, Inc.     

Dendritic cell activation prevents MHC class II ubiquitination and promotes MHC class II survival regardless of the activation stimulus

The expression of MHC class II (MHC-II) on the surface of antigen-presenting cells, such as dendritic cells (DCs), is tightly regulated during cellular activation. Many cells, including DCs, are activated following stimulation of innate Toll-like receptors (TLRs) by products of microorganisms. In the resting (immature) state, MHC-II is ubiquitinated in immature DCs and is rapidly degraded; however, after activation of these cells with MyD88-dependent TLR ligands, MHC-II ubiquitination is blocked, and MHC-II survival is prolonged. We now show that DC activation using MyD88-dependent TLR ligands, MyD88-independent TLR ligands, and even infection with the intracellular parasite Toxoplasma gondii leads to identical changes in MHC-II expression, ubiquitination, and surface stability, revealing a conserved role for enhanced MHC-II stability after DC activation by different stimuli.     

A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.     

Deterministic epidemiological models at the individual level

In many fields of science including population dynamics, the vast state spaces inhabited by all but the very simplest of systems can preclude a deterministic analysis. Here, a class of approximate deterministic models is introduced into the field of epidemiology that reduces this state space to one that is numerically feasible. However, these reduced state space master equations do not in general form a closed set. To resolve this, the equations are approximated using closure approximations. This process results in a method for constructing deterministic differential equation models with a potentially large scope of application including dynamic directed contact networks and heterogeneous systems using time dependent parameters. The method is exemplified in the case of an SIR (susceptible-infectious-removed) epidemiological model and is numerically evaluated on a range of networks from spatially local to random. In the context of epidemics propagated on contact networks, this work assists in clarifying the link between stochastic simulation and traditional population level deterministic models.     

Cell contact-dependent functional selectivity of β2-adrenergic receptor ligands in stimulating cAMP accumulation and extracellular signal-regulated kinase phosphorylation

Activation of β(2)-adrenegic receptor (β(2)-AR) leads to an increase in intracellular cAMP and activation of ERK. These two signals are activated by the interaction of the receptor with different transducer partners. We showed that the intrinsic activities of β(2)-AR ligands for stimulating cAMP production and ERK phosphorylation responses in HEK-293 cells were not correlated. The lack of correlation resulted mainly from the discrepancy between the intrinsic activities of two groups of ligands for these two responses: The first group consisted of clenbuterol, cimaterol, procaterol, and terbutaline which acted as full agonists for cAMP production but displayed very weak effect on ERK phosphorylation. The second group comprised adrenaline and noradrenaline which displayed higher intrinsic activity for the ERK phosphorylation than for the cAMP response. Thus, both groups behaved as functionally selective ligands. The functional selectivity of the first group was observable only in adherent cells when confluence was approximately 100%. When cell-cell contact was minimized either by decreasing the density of the adherent cells or by bringing the cells into suspension, the first group of ligands gained the ability to stimulate ERK phosphorylation without a change in their effect on cAMP production. In contrast, selectivity of the second group was independent of the adherence state of the cells. Our results show that the inherent "bias" of ligands in coupling a G protein-coupled receptor to different transducers may not always be revealed as functional selectivity when there is a "cross-talk" between the signaling pathways activated by the same receptor.     

Analysis of cell locomotion

The methods of statistical physics have been applied to the analysis of cell movement. Human polymorphonuclear leukocytes were exposed to different surfaces possessing parallel oriented physical stuctures (scratched glass surface, machine drilled aluminium surface, optical grid and stretched polyethylene foil) and cell migration was observed using time-lapse photography.We demonstrate that in cell migration along physical structures, referred to as contact guidance, two subgroups can be distinguished: 1) The nematic type where the cell size is large in relation to the grid distance of the undulate surface. 2) The smectic type where the cell size is small in relation to the grid distance of the substrate.Nematic contact guidance is characterized by an anisotropic random walk. In all substrates investigated the diffusion process parallel to the lines was faster than the diffusion process perpendicular to them. The angular dependent diffusion coefficient was described by an ellipse. Deviation from a circle defined an apolar order parameter, whose value was about 0.3. The amount of information which the cells collected from, the undulate surface was very low, between 0.1 and 0.2 bits. We demonstrate that cells do not recognize all the details of their surroundings and that their migration can be compared to the groping around of a short sighted man. The blurred environment can be described by a mean field whose strength is proportional to the aploar order parameter. It is argued that the anisotropic surface tension is the basic source for nematic contact guidance.Smectic contact guidance is characterized by an anisotropic random walk and is quantified by a density order paramter which is 0.28 in the case of the scratched glass surface of a Neubauer counting chamber. The information which the cells collect from their environment is very low (0.03 bits). The lines seen by the cell can be described by a mean field whose strength is proportional to the density oder parameter.Finally, we demonstrate that the locomotion of granulocytes is governed by an internal clock and internal programs. After migrating for a certain time (32 s) in a particular direction, a new direction of locomotion is determined by an internal program. The cell decides basically between left or right, thereby preferring a turn angle such that the cell migrates either parallel or perpendicular to the lines. the angles are nearly equally probable but the cell moves, in the case of nematic guidance, with different velocities in the +or-direction. The cell also has directional memories with characteristic times of 32 s and greater than 100 s.     

A method to fabricate mesoscopic freestanding polydimethylsiloxane membranes used to probe the rheology of an epithelial sheet

Details are presented for the formulation, fabrication, and mechanical characterization of mesoscopic freestanding polydimethylsiloxane (PDMS) elastomer membranes, 10.0 μm thick and 5.0 mm in diameter, used to probe the rheology of a living epithelial sheet. In what is described as a composite diaphragm inflation (CDI) experiment, freestanding PDMS membranes are utilized as substrates for the culture of a sheet of epithelial cells. Together, the cell layer and the PDMS elastomer form a composite diaphragm (CD) that is suitable for mechanical testing in an axisymmetric membrane inflation experiment. In order to distinguish the rheological behavior of the epithelial sheet from the mechanical response of the elastomer using inflation test data, freestanding PDMS membranes should exhibit a highly compliant yet mechanically invariant finite load-deformation response when subjected to multiple inflation cycles following intermittent periods of cell culture. Given these considerations, we describe a method for preparing freestanding PDMS elastomer membrane specimens that are optically transparent, tensed, and wrinkle-free. Surface modifications intended to facilitate cell culture, namely water vapor plasma and ultraviolet light treatments, were shown to dramatically stiffen the mechanical response of the membranes, rendering them unusable as CD substrates. In this study, only PDMS membranes with physiosorbed collagen demonstrated the mechanical compliance, fatigue resistance, and environmental stability necessary for reliable use in CDI experiments.     

Human lymphocyte migration in vitro: characterization and quantitation of locomotory parameters.

Using a time-lapse cinephotomicrographic technique, the locomotory paths taken by lymphocytes have been shown to satisfy the requirements for a continuous-time Markov chain analysis consisting of four directional states defined by the four quadrants of a Cartesian plane and state 0 in which the cells are stationary. The important parameters characterizing this path motion are the average time (waiting time) that a cell spends in each state and the state transition probabilites which, using the Markov model, allow the computation of the probability of the cells moving in a given direction. Our results show that lymphocytes moving alone on glass exhibit a random migration pattern.     

DNA damage response is suppressed by the high cyclin-dependent kinase 1 activity in mitotic mammalian cells

DNA damage response (DDR) is vital for genomic stability, and its deficiency is linked to tumorigenesis. Extensive studies in interphase (G(1)-S-G(2)) mammalian cells have revealed the mechanisms of DDR in great detail; however, how mitotic cells respond to DNA damage remains less defined. We report here that a full DDR is suppressed in mitotic mammalian cells until telophase/cytokinesis. Although early DDR markers such as the phosphorylations of ataxia telangiectasia mutated (ATM) and histone H2A.x (H2AX) can be readily detected, the ionizing radiation-induced foci (IRIF) formation of late DDR markers such as breast cancer type 1 susceptibility protein (BRCA1) and p53-binding protein 1 (53BP1) are absent until the telophase/cytokinesis stage. We further showed that the IR-induced ubiquitination cascade around DNA damage sites did not occur in mitotic cells, which explains, at least in part, why BRCA1 and 53BP1 cannot be recruited to the damaged sites. These observations indicate that DDR is suppressed in mitotic cells after the step of γH2AX formation. Not surprisingly, we found that the absence of a full DDR in mitotic cells was associated with the high cyclin-dependent kinase 1 (CDK1) activities. More 53BP1 IRIF could be detected when the irradiated mitotic cells were treated with a CDK1 inhibitor. Further, the activation of CDK5 in interphase cells impedes the formation of 53BP1 IRIF. Together, these results suggest that the DDR is suppressed by the high CDK1 activity in mitotic mammalian cells.     

Evaluating the nucleus effect on the dynamic indentation behavior of cells

The effect of the nucleus on the cell mechanical behavior was investigated based on the dynamic indentation response of cells under a spherical tip. A “two-component” cell model (including cytoplasm and nucleus) is used, and the dynamic indentation behavior is studied by a semiempirical method, which is established based on fitting the numerical simulation results of the quasi-static indentation response of cells. We found that the “routine analysis” (based on the Hertz’s contact solution of homogeneous model) significantly overestimated the nucleus effect on the overall cell indentation response due to the effects of the Hertz contact radius and the substrate stiffening. These effects are significantly stronger in the “two-component” cell model than in the homogeneous model. The inaccuracy created by the “routine analysis” slightly increases with the modulus ratio of nucleus to cytoplasm and the volume fraction of nucleus. Finally, the error sensitivity to the geometrical parameters used in the model is discussed, which shows the indentation analysis is not very sensitive to these parameters, and the reasonable assumptions for these parameters are effective. This systematic analysis can provide a useful guideline to understanding the mechanical behavior of cells and nuclei.